Access Stage results in Workflow/ Pipeline plugin

You definitely could use Pipeline REST API Plugin, for me it was available out of the box with Jenkins 2.13.

By parsing the resulting JSON you could get the status of the stage similarly to what you expect. For the api call I personally use http_request plugin.

From the documentation GET /job/:job-name/:run-id/wfapi/describe returns:

{
    "_links": {
        "self": {
            "href": "/jenkins/job/Test%20Workflow/16/wfapi/describe"
        },
        "pendingInputActions": {
            "href": "/jenkins/job/Test%20Workflow/16/wfapi/pendingInputActions"
        }
    },
    "id": "2014-10-16_13-07-52",
    "name": "#16",
    "status": "PAUSED_PENDING_INPUT",
    "startTimeMillis": 1413461275770,
    "endTimeMillis": 1413461285999,
    "durationMillis": 10229,
    "stages": [
        {
            "_links": {
                "self": {
                    "href": "/jenkins/job/Test%20Workflow/16/execution/node/5/wfapi/describe"
                }
            },
            "id": "5",
            "name": "Build",
            "status": "SUCCESS",
            "startTimeMillis": 1413461275770,
            "durationMillis": 5228
        },
        {
            "_links": {
                "self": {
                    "href": "/jenkins/job/Test%20Workflow/16/execution/node/8/wfapi/describe"
                }
            },
            "id": "8",
            "name": "Test",
            "status": "SUCCESS",
            "startTimeMillis": 1413461280998,
            "durationMillis": 4994
        },
        {
            "_links": {
                "self": {
                    "href": "/jenkins/job/Test%20Workflow/16/execution/node/10/wfapi/describe"
                }
            },
            "id": "10",
            "name": "Deploy",
            "status": "PAUSED_PENDING_INPUT",
            "startTimeMillis": 1413461285992,
            "durationMillis": 7
        }
    ]
}

You can iterate all stages of the build and do what you need:

    WorkflowRun run = Jenkins.instance.getItemByFullName("####YOUR_JOB_NAME####")._getRuns()[0]
    FlowExecution exec = run.getExecution()
    PipelineNodeGraphVisitor visitor = new PipelineNodeGraphVisitor(run)
    def flowNodes = visitor.getPipelineNodes()

    for (Iterator iterator = flowNodes.iterator(); iterator.hasNext();)
    {
        def node = iterator.next()
        if (node.getType() == FlowNodeWrapper.NodeType.STAGE)
        {
               String stageName = node.getDisplayName()
               def stageResult = node.getStatus().getResult()

               println "Result of stage ${stageName} is ${stageResult}"
        }
    }